I have included a waypoint for the suggested parking lot. The other lot is often filled by groups renting the facilities and by Zoo parking. If this lot is also full, you may also park along most of Broadway Street (obey parking signs).
Begin your adventure at the indicated coordinates. Use your GPSr/phone to project a waypoint 200 feet to the Southeast (degree 135). Proceed to that second waypoint. There you will find a great place to sit and take in the view. This location is between a few of the obvious stairways in the park. Now walk back in the direction that you just came from until you reach a paved pathway. You must choose to go either left or right. However, if you make the right choice, you would be wrong, so try to be correct. Soon you will be passing a brick building. At that location, there is a small clearing along the woodline. Enter that clearing. There will be a fallen tree to the left and to the right there is a small incline to another level that is about 5 feet lower. Walk down that hill. As soon as you reach that lower level, look to the right into the treeline. There you will find the top of an old abandoned stairway that is reverting back to nature. Make your way down that stairway until you come to a large dead tree. There you will find the object you are looking for by utilizing your geosenses. In the container you will find a stamp and ink pad. These are not trade items and should remain in the geocache.